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6 Wave equation in spherical polar coordinates
www2.ph.ed.ac.uk6 Wave equation in spherical polar coordinates We now look at solving problems involving the Laplacian in spherical polar coordinates. The angular dependence of the solutions will be described by spherical harmonics. We take the wave equation as a special case: ∇2u = 1 c 2 ∂2u ∂t The Laplacian given by Eqn. (4.11) can be rewritten as: ∇ ...
1. Vectors, contravariant and covariant
www.seas.upenn.eduone system of coordinates may be transformed into V0in a new system of coordinates. The upper index is the row and the lower index is the column, so for contravariant transformations, is the ... in spherical corrdinates @^r @ 6= ^ @r. The Christo el symbol is symmetric in its two lower indices: k ij = k ji. m ij = 1 2 em @e i @xj + 1 2 em @e = 1